I don't think they are going to throw extra money at Vesey. Usually the Rangers look at what the other RFAs that have similar stats are getting, or have received, for bridges and they offer something in that range, because that is what the player would get if he went through with arbitration anyway.
For example, Josh Anderson may be a comparable player in stats, he ended up signing for 3 years at a 1.85M cap hit. If the Rangers go two years its going to be a little cheaper than that. So while I said above like 1.2M, 1.5M or so may be the better range based on that comparable.
Miller is different, he is going to get a contract that is higher than seems normal because he only has one RFA year left. Rangers have far less leverage there. He could go to arbitration, take the one year award and be a pure UFA the very next off season. Usually the player and team hedge their bets, player wants the security of a bigger guaranteed contract so will take a little less, team owns their rights longer so will pay a little more, all gets wrapped up in some compromise.